Geodesic
Periodic Solutions of Periodic Retarded Functional Differential Equations
Marcin Pawłowski1
1 Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 4, pp. 353-363.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The paper presents a geometric method of finding periodic solutions of retarded functional differential equations (RFDE) $x'(t) = f(t, x_{t})$, where $f$ is $T$-periodic in $t$. We construct a pair of subsets of ${\mathbb R} \times {\mathbb R}^{n}$ called a $T$-periodic block and compute its Lefschetz number. If it is nonzero, then there exists a $T$-periodic solution.
DOI : 10.4064/ba52-4-2
Keywords: paper presents geometric method finding periodic solutions retarded functional differential equations rfde where t periodic construct pair subsets mathbb times mathbb called t periodic block compute its lefschetz number nonzero there exists t periodic solution

Marcin Pawłowski 1

1 Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland 
@article{10_4064_ba52_4_2,
     author = {Marcin Paw{\l}owski},
     title = {Periodic {Solutions} of {Periodic} {Retarded} {Functional} {Differential} {Equations}},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     pages = {353--363},
     publisher = {mathdoc},
     volume = {52},
     number = {4},
     year = {2004},
     doi = {10.4064/ba52-4-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ba52-4-2/}
}
TY  - JOUR
AU  - Marcin Pawłowski
TI  - Periodic Solutions of Periodic Retarded Functional Differential Equations
JO  - Bulletin of the Polish Academy of Sciences. Mathematics
PY  - 2004
SP  - 353
EP  - 363
VL  - 52
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ba52-4-2/
DO  - 10.4064/ba52-4-2
LA  - en
ID  - 10_4064_ba52_4_2
ER  - 
%0 Journal Article
%A Marcin Pawłowski
%T Periodic Solutions of Periodic Retarded Functional Differential Equations
%J Bulletin of the Polish Academy of Sciences. Mathematics
%D 2004
%P 353-363
%V 52
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ba52-4-2/
%R 10.4064/ba52-4-2
%G en
%F 10_4064_ba52_4_2
Marcin Pawłowski. Periodic Solutions of Periodic Retarded Functional Differential Equations. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 4, pp. 353-363. doi : 10.4064/ba52-4-2. http://geodesic.mathdoc.fr/articles/10.4064/ba52-4-2/

Cité par Sources :